Method for determining the equivalency index of goods, processes, and services

ABSTRACT

A method is disclosed wherewith a person skilled in the art of statistical quality control may determine whether a process, goods, or service is statistically equivalent to another of known quality, or to a desired target quality. The method may also be used to determine whether multiplicities of goods, processes, or services are statistically equivalent to one another and of a desired quality. The method makes the determination based on an equivalency index that is derived from integration of the probability distribution of data of measurement taken from products associated with the process, goods or services.

This is a divisional application of Ser. No. 10/164,519 filed Jun. 6,2002 now U.S. Pat. No. 6,789,031.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention is related to field of statistical quality control andmore specifically related to a method of determining an equivalencyindex of goods, processes and services.

2. Description of the Related Art

Every goods, process and service possess a number of parameters thatjointly describe what the user thinks of as quality. These parametersare often called quality characteristics. Quality characteristics may bephysical such as length, weight, voltage, and viscosity, or sensory suchas taste, appearance, color, and ease of use, or time orientation suchas reliability, and durability.

In the past, the buyers had to carry the burden of examining, judging,and testing goods for themselves. Competition in the market place hasshifted the burden to the producers. The producers not only must screenout the non-conforming products before they reach the customers, theymust continuously monitor their manufacturing processes for continuousquality improvement in order to compete.

To aid such endeavor, statistical tools have been developed. Today, itis common for the producers of goods such as automobile, computer,clothing, and its field service and provider of services such asgeneration and distribution of electrical energy, Internet services,telephone services, public transportation, banking, health, andaccounting to adopt statistical quality control tools in their routinebusiness and manufacturing operation. Such tools have becomeindispensable in their endeavor to compete for market share.

Among the tools that are prevalent among the practitioners ofstatistical quality control are the control chart, the Pareto diagram,the scatter plot, the histogram, the experimental design, and theacceptance sampling.

One common character of these tools is that they are most effective whenused to correlate between characteristic quality parameters of aproduct, be it goods or service, and the input or process parametersthat can affect the quality parameters. Practitioners use these tools tocompare the variation of the quality parameters to the predeterminedlimits and to distinguish between common and special causes so as tounderstand and analyze the variation in the quality of a goods orservice. Once the causes are identified, the information enables thepractitioner to make necessary modification in order to control theeffect and reduce the variation. These tools, however, have a commonshortcoming.

In today's business environment, producers may be manufacturing theirgoods in many production sites, often in distant parts of the world.Service providers may also provide their products in many diversegeographical locations. Yet, the goods and service must be controlled tothe same quality standard. A customer will expect the same quality offood and service from a restaurant in Tokyo, Japan as he receives inQuadalajara, Mexico if the restaurants bear the same name. Amicro-controller chip maker in Taiwan who tries to qualify as a supplierto a German company must demonstrate that its chips meet the customer'sspecification and are equal, statistically speaking, to the parts thecustomer currently uses. The traditional statistical quality controlmethods and tools are less helpful for such purposes. When the issueconcerns the degree of equivalency among a multiplicity of items ofgoods, processes, and services, it is difficult, with such tools, toreach an unambiguous conclusion readily and to express the conclusion asa concise numerical format.

BRIEF SUMMARY OF THE INVENTION

It is the object of this invention to provide a method with which aperson of ordinary skill in the area of statistical quality control candetermine whether a goods, process, or service is statisticallyequivalent to another of known quality.

It is also the object of this invention to provide a method with which aperson of ordinary skill in the area of statistical quality control candetermine whether a goods, process, or service is statisticallyequivalent to a required standard.

It is also the object of this invention to provide a method with which aperson of ordinary skill in the area of statistical quality control candetermine whether a multiplicity of goods, processes, or services arestatistically equivalent to one another and of a desired quality.

Examples of such occasion are abundant: an owner or operator of a plantmay need to judge the quality of a potential electricity supplier interms of fluctuation of the supply voltage over time and compare that tothe current supplier, an electronic system maker may need to judge thequality equivalency of the printed circuit board from a new vendors interms of the thickness variation of the board in view of his productionequipment specifications, other examples are the fill volume of softdrink beverage from various bottling machines, the net weight of a dryleach product from multiple production lines, the tensile strength ofalternative new alloy materials for an automotive engine part, the timeto failure of an electronic component from different vendors, or theresults of many quality-control technicians measuring the surface finishof a metal parts.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts the steps of a method for declaring a process in twosemiconductor IC fabrication facilities A and B (FABs A and B) to beequivalent in quality based on equivalency indices.

FIG. 2 depicts the steps of a method for declaring a process in asemiconductor IC fabrication facility as being equivalent in quality toa baseline process based on equivalency indices.

FIG. 3 depicts the steps of a method for declaring a plurality ofsemiconductor IC fabrication facilities as being equivalent in qualitybased on equivalency indices.

FIG. 4 depicts two probability distribution curves. One curve isgenerated from measurements taken from products of a semiconductor ICfabrication facility. FABs A the other curve is from PAB B.

FIG. 5 depicts the passing and failing thresholds on an equivalencyindex scale and the corresponding scale measuring the separation betweentwo probability distributions.

FIG. 6 depicts two probability distribution curves. the other curve is abaseline facility LAB L.

FIG. 7 depicts three probability distribution curves. One curve isgenerated from measurements taken from products of a semiconductor ICfabrication facility. FABs A, the second curve is from FAB B and thethird curve is from FAB C. Also depicted is the target value T of theparameter.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 depicts a specific example of the first embodiment of thisinvention, a method with which a semiconductor manufacturer maydetermine whether two of its integrated circuit (IC) manufacturingfacilities (FABs) produce an IC product that is statisticallyequivalent. The two FABs may or may not have identical type and model ofmanufacturing equipment, they may or may not share identical recipe ofmanufacturing process. Although the method is illustrated withsemiconductor IC product, this method can easily apply to other type ofproducts. This method is also not limited to manufactured goods but caneasily apply to services. What is required is a set of identifiable,measurable parameters that jointly describe what the user thinks of asquality of the product. A person skilled in the art of statisticalquality control would be able to adopt this method to his or her ownsituation with equal effectiveness, regardless of which type of goods orservice is being produced. This principle also applies to the otherembodiment of this invention.

In step 101, the method requires one to identify one or more variableparameters that are characteristic of the IC manufacturing process,which can be measured from a product manufactured with the process. Thenumber of parameters that are necessary to make this equivalencydetermination may be large or small, depending on the complexity of theprocess and the economy of the operation. In modern semiconductorintegrated circuit products, one may choose among parameters related toa typical transistor in the integrated circuit, such as the transistorchannel length, the gate oxide thickness, the drive current, gate tosubstrate leakage current etc.

In step 102, one takes measurements of an identified parameter in step101, for instance, the transistor drive current from a group of ICproducts manufactured in a first facility, FAB A. The measurement mayrequire hand probing by an operator if the desired sample size is small.

Otherwise, it may require an automated system that incorporatesautomated testing system for data acquisition and computer system fordata crunching.

In step 103, one records the data from the measurements. Again,depending on the sample size, the recording may be in a laboratorynotebook, a personal computer, or a fully automated system.

In step 104, one constructs a probability distribution curve from thedata recorded in step 103. Element 401 of FIG. 4 depicts such adistribution curve. Depending on the nature of the parameter, the datamay form different types of distribution. The most common distributionis the normal distribution or the bell-curve distribution. Other typesof distribution encountered in a typical manufacturing process includebinomial, chi-square, t, F, exponential, gamma, Pascal, Poisson andWeibull distribution. The method described here works well with normaland other types of discrete and continuous distributions. In case thedistribution does not conform to a commonly recognizable model, a personskilled in the art of statistical quality control will be able to usenumerical method or graphical method in implementing the teachingdisclosed in this invention.

In step 105, one extracts the average and the standard deviation fromthe probability distribution. The extraction may be accomplishedmanually or by a computer. It is familiar to a person skilled in the artof statistical quality control.

In step 106, 107, 108, and 109, one repeats the procedure of measurementand extraction on a group of products manufactured in a second facility,FAB B. FIG. 4, element 402 depicts a probability distribution curve fromFAB B.

With the two curves showing in the same drawing, one can readily observequalitatively the overlapping of the probability distribution. The morethe two curves overlap, the more similar the products from of the twofacilities are. The degree of the overlap of the curves, therefore,serves as a good indication of the equivalency of the two processesunder comparison. The remaining of the method quantifies the equivalencyby performing an integration of the probability distributions over aproper range.

In step 110, one chooses the range limits of the integration. In thisexample, the chosen limits are the three-sigma points of the two curves.The concept of three-sigma is familiar to a person skilled instatistical quality control. The upper limit of the integration ischosen to be the lesser of the two three-sigma points that are the upperlimit of 99.7% inclusion of all data points under the curves. The lowerlimit is the greater of the two three sigma points that are the lowerlimit of 99.7% inclusion of all data point under the two curves. In FIG.4, the upper and lower limits are designated as D, element 412, and C,411 respectively.

In step 111, one carries out the integration of the sum of the twoprobability distribution functions. When the two distributions arenormal distribution, the result of the integration lies between 2×99.7%and 2×0.3%. In a mathematical form the integration may be written as

$E_{PAB} = {{\left( {\frac{1}{2}{\int_{C}^{D}{\left\lbrack {{f_{A}(x)} + {f_{B}(x)}} \right\rbrack\ {\mathbb{d}x}}}} \right)/99.7}\%}$where E_(PAB) is the equivalency index of the parameter P of FABs A andB, D is element 412 in FIG. 4, the upper three-sigma point of element402, C is element 411 in FIG. 4, the lower three-sigma point of element401, f_(A)(x) is the probability distribution function of data from FABA, element 401 in FIG. 4, f_(B)(x) is the probability distributionfunction of data from FAB B, element 402 in FIG. 4.

In step 112, a division by a weighing factor of 2×99.7% normalizes theresult of the integration to yield a number between 100% and less than1%. The purpose of the normalization is for the ease of automation.Choice of other weighing factors is also possible. Otherwise, thenormalization may also be omitted.

In step 114, this number is defined as the equivalency index of theparameter under test.

In step 115, one sets the thresholds to delineate the ranges of passingand failing of an equivalent index. In this example, passing is set at98% and failing is set at 90%. These particular threshold values arechosen because according to the current semiconductor industry practice,when two probability curves plotting data generated form two groups ofproducts, are within one sigma shift distant apart, the two groups ofproducts are considered as not statistically significantly differentfrom each other. If, however, the distance is more than a two-sigmashift, the two groups are considered to be significantly different. Thethreshold value of 98%, as shown in FIG. 5, conveniently corresponds toa one-sigma shift and the value of 90% is very closely corresponding toa two-sigma shift between the two probability distribution curves.

While there is a statistical base for choosing these threshold values,the method disclosed in this invention is equally effective with otherchoice of the threshold values based on other considerations such ascustom or economy. Also, this step may be performed temporallyindependent of other steps in the method. If the same considerationapplies for all the identified parameters under consideration, the sameset of threshold values may be used. Otherwise, one may choose to usedifferent threshold values for different parameters.

FIG. 5 depicts the relationship between values of an equivalency indexand the corresponding shift of two probability distribution curves thatgenerate the equivalency index. Element 501 depicts the scale ofequivalency indices and element 502 depicts the scale of thecorresponding shift.

In step 116, one compares the equivalency index E_(PAB) to the rangesset in step 115. If E_(PAB) is in the range above the upper thresholdvalue of 98%, the passing range or a green zone, one would declare thatFABs A and B are equivalent in quality with respect to parameter P. Onthe other hand, if E_(PAB) is in the range below the lower thresholdvalue of 90%, a failing range or a red zone, one would declare that FABsA and B are not equivalent in quality with respect to parameter P. Anequivalency index that falls between 98% and 90%, or a yellow zone,usually calls for reviewing of the data and the procedure.

In step 117, the method requires a repeat of steps 102 to 106 for theremaining identified parameters.

In step 118, one declares that in regarding the product being tested,FABs A and B are equivalent in quality when the equivalency indices ofthe pre-identified set of parameters are all in the passing range.

FIG. 2 depicts another embodiment of the invention, a method fordetermining whether a process in a semiconductor IC fabrication facility(FAB F) is equivalent in quality to a baseline process of anotherfacility (LAB L) based on Equivalency Indices. The method is similar inmany aspects to the method of FIG. 1. The main difference is that withthis method, one compares a facility of unknown quality to a baselineprocess of known quality. A laboratory is used in this embodiment toprovide the baseline process but the method applies equally well whenthe baseline of known quality is from an established manufacturingplant, or from results of computer simulation.

As with the method in FIG. 1, the generation of an equivalency indexrequires an integration operation, performed either manually or througha machine. Because the comparison is against a baseline of knownquality, the limits of integration will be chosen to be the 3-sigmapoints of the baseline. If the products under test have a smallerstandard deviation than that of the baseline process, it is possible forthe equivalency index of the facility under test to be greater than100%.

In step 201, the method requires one to identify one or more variableparameters that are characteristic of the IC manufacturing process andthat can be measured from a product manufactured with the process. Thenumber of parameters that are necessary to make this equivalencydetermination may be large or small, depending on the complexity of theprocess and the economy of the operation. In modern semiconductorintegrated circuit products, one may choose among parameters related toa typical transistor in the integrated circuit, such as the transistorchannel length, the gate oxide thickness, the drive current, gate tosubstrate leakage current etc.

In step 202, one takes measurements of an identified parameter in step201, for instance, the transistor drive current from a group of ICproducts manufactured in a first facility. FAB F. The measurement mayrequire hand probing by an operator if the desired sample size is small.Otherwise, it may require an automated system that incorporatesautomated testing system or data acquisition and computer system fordata crunching.

In step 203, one records the data from the measurements. Again,depending on the sample size, the recording may be in a laboratorynotebook, a personal computer, or a fully automated system.

In step 204, one constructs a probability distribution curve from thedata recorded in step 203. Element 601 of FIG. 6 depicts such adistribution curve. Depending on the nature of the parameter, the datamay form different types of distribution. The most common distributionis the normal distribution or the bell-curve distribution. Other typesof distribution encountered in a typical manufacturing process includebinomial, chi-square, t, F, exponential, gamma, Pascal, Poisson andWeibull distribution. The method described here works well with normaland other types of discrete and continuous distributions. In case thedistribution does not conform to a commonly recognizable model, a personskilled in the art of statistical quality control will be able to usenumerical method or graphical method in implementing the teachingdisclosed in this invention.

In step 205, one extracts the average and the standard deviation fromthe probability distribution. The extraction may be accomplishedmanually or by a computer. It is familiar to a person skilled in the artof statistical quality control.

In step 206, one provides the baseline process information. The baselinemay be from a batch of prototype product fabricated in a laboratory asin this example. It may be information gathered from a production run ofan established factory or it may be from computer simulation. What isrequired of the baseline process is a distribution curve with associatedaverage and standard deviation against which the facility under testwill be compared. A baseline distribution curve is depicted as element601 in FIG. 6.

In step 207 one performs the integration of the distribution curvegenerated in step 204 and depicted as element 602 in FIG. 6. Note thatthe limits of integration C, element 611, and D, element 612 in FIG. 6are the 3-sigma points of curve 601 of the baseline. The integrationoperation is usually performed by a machine. In simple cases, it may beperformed manually.

In a mathematical form the integration may be written asEp=(∫ _(C) ^(D) f _(p)(x)dx)/99.7%,where E_(p) is the equivalent index of parameter P of FAB F, C and D arethe 3-sigma points 611 and 612 of the probability distribution curve 601in FIG. 6, f_(p)(x) is the probability distribution function 602 in FIG.6. 99.7% is a weighing factor that will be discussed in step 208.

In step 208, one normalizes the result of the integration. In thisexample, one uses a weighing factor of 99.7%. If the distribution undertest matches the distribution of the baseline perfectly, thenormalization would yield an number of 100%. The choice of 99.7% is aconvenient one and it is consistent with the custom of currentsemiconductor industry practice. One may choose a weighing factor otherthan 99.7% or omit the normalization step without deviating from theteaching of this method.

In step 209, this number is defined as the equivalency index of theparameter under test.

In step 210, one sets the thresholds to delineate the ranges of passingand failing of an equivalent index. In this example, passing is set at98% and failing is set at 90%.

These particular threshold values are chosen because according to thecurrent semiconductor industry practice, when two probability curvesplotting data generated form two groups of products, are within onesigma shift distant apart, the two groups of products are considered asnot statistically significantly different from each other. If, however,the distance is more than a two-sigma shift, the two groups areconsidered to be significantly different. The threshold value of 98%, asshown in FIG. 5, conveniently corresponds to a one-sigma shift and thevalue of 90% is very closely corresponding to a two-sigma shift betweenthe two probability distribution curves.

While there is a statistical base for choosing these threshold values,the method disclosed in this invention is equally effective with otherchoice of the threshold values based on other considerations such ascustom or economy. Also, this step may be performed temporallyindependent of other steps in the method. If the same considerationapplies for all the identified parameters under consideration, the sameset of threshold values may be used. Otherwise, one may choose to usedifferent threshold values for different parameters.

FIG. 5 depicts the relationship between values of an equivalency indexand the corresponding shift of two probability distribution curves thatgenerate the equivalency index. Element 501 depicts the scale ofequivalency indices and element 502 depicts the scale of thecorresponding shift.

In step 211, one compares the equivalency index E_(P) to the ranges setin step 210. If E_(P) is in the range above the upper threshold value of98%, the passing range or a green zone, one would declare that FAB F isequivalent in quality to LAB L with respect to parameter P. On the otherhand, if E_(P) is in the range below the lower threshold value of 90%, afailing range or a red zone, one would declare that FAB F is notequivalent in quality to LAB L with respect to parameter P. Anequivalency index that falls between 98% and 90%, or a yellow zone,usually calls for reviewing of the data and the procedure.

In step 212, the method requires one to repeat steps 201 to 211 for theremaining identified parameters.

In step 213, one declares that in regarding the product being tested,FAB F and LAB L are equivalent in quality when the equivalency indicesof the pre-determined set of parameters all are in the passing range.

FIG. 3 depicts yet another embodiment of the invention, a method fordetermining, with respect to one particular manufacturing process thathas been installed in a group of manufacturing facilities (FABs A, B,and C), which FABs are producing products that are equivalent inquality. The method is similar in many aspects as the method depicted inFIG. 1 and FIG. 2. In particular, like the method of FIG. 1, it does notrequire a baseline distribution except it does require a baseline targetvalue for the parameter. But unlike the method of FIG. 1, it compares aplurality of facilities instead of two facilities. Like the method inFIG. 2, the integration limits are picked from one particularprobability distribution instead of a combination of distributions.

In step 301, the method requires one to identify one or more variableparameters that are characteristic of the IC manufacturing process andthat can be measured from a product manufactured with the process. Thenumber of parameters that are necessary to make this equivalencydetermination may be large or small, depending on the complexity of theprocess and the economy of the operation. In modem semiconductorintegrated circuit products, one may choose among parameters related toa typical transistor in the integrated circuit, such as the transistorchannel length, the gate oxide thickness, the drive current, gate tosubstrate leakage current etc.

In step 302, one takes measurements of an identified parameter in step301, for instance, the transistor drive current from a group of ICproducts manufactured in a first facility. FAB A. The measurement mayrequire hand probing by an operator if the desired sample size is small.Otherwise, it may require an automated system that incorporatesautomated testing system for data acquisition and computer system fordata crunching.

In step 303, one records the data from the measurements. Again,depending on the sample size, the recording may be in a laboratorynotebook, a personal computer, or a fully automated system.

In step 304, one constructs a probability distribution curve from thedata recorded in step 303. Element 701 of FIG. 7 depicts such adistribution curve. Depending on the nature of the parameter, the datamay form different types of distribution. The most common distributionis the normal distribution or the bell-curve distribution. Other typesof distribution encountered in a typical manufacturing process includebinomial, chi-square, t, F, exponential, gamma, Pascal, Poisson andWeibull distribution. The method described here works well with normaland other types of discrete and continuous distributions. In case thedistribution does not conform to a commonly recognizable model, a personskilled in the art of statistical quality control will be able to usenumerical method or graphical method in implementing the teachingdisclosed in -his invention.

In step 305, one extracts the average and the standard deviation fromthe probability distribution. The extraction may be accomplishedmanually or by a computer. It is familiar to a person skilled in the artof statistical quality control.

In step 306, one repeats the steps 302 to 305 on products from FABs Band C.

In step 307, one compares the distributions of FABs A, B, and C todetermine on one FAB of which the measured data have the smalleststandard deviation. This sets the standard of variation against whichall facilities will be judged. If, however, due to other considerationsuch as cost, an alternative standard is more desirable, the choice ofsuch standard would not diminish the effectiveness of this method.

In step 311 one performs the integration of the distribution curvesgenerated in step 304 and depicted as element 701 in FIG. 7. Note thatthe limits of integration C, element 711 and D, element 712 in FIG. 7are related to the 3-sigma points of curve 701 that has the smalleststandard deviation. The same limits C and D will be used in theintegration of all other probability distribution functions of otherFABs. The lower limit C, element 711, and the higher limit D, element712 are set atC=T−3×Sigma_(MIN);D=T+3×Sigma_(MIN),

where C is the lower limit of the integration 711, T is the target valuefor parameter P 713, Sigma_(MIN) is the standard deviation of curve 701,and D is the upper limit of the integration, 712.

The integration operation is usually performed by a machine. In simplecases, it may be performed manually.

In a mathematical form the integration may be written asEpa=(∫_(C) ^(D) [f _(A)(x)]dx)/99.7%,where E_(pa) is the equivalent index of parameter P of FAB A, f_(A)(x)is the probability distribution function 701, in FIG. 7 and 99.7% is theweighing factor and will be explained in step 312.

In step 312, a division by a weighing factor of 99.7% normalizes theresult of the integration to yield a number between 100% and less than1%. The purpose of the normalization is for the ease of automation.Choice of other weighing factors is also possible. Otherwise, thenormalization may also be omitted.

In step 313, one designates the result of the integration and thenormalization E_(PA) as the equivalent index for parameter P of the FABA under test.

In step 314, one sets the thresholds to delineate the ranges of passingand failing of an equivalent index. In this example, passing is set at98% and failing is set at 90%. These particular threshold values arechosen because according to the current semiconductor industry practice,when two probability curves plotting data generated form two groups ofproducts, are within one sigma shift distant apart, the two groups ofproducts are considered as not statistically significantly differentfrom each other. If, however, the distance is more than a two-sigmashift, the two groups are considered to be significantly different. Thethreshold value of 98%, as shown in FIG. 5, conveniently corresponds toa one-sigma shift and the value of 90% is very closely corresponding toa two-sigma shift between the two probability distribution curves.

While there is a statistical base for choosing these threshold values,the method disclosed in this invention is equally effective with otherchoice of the threshold values based on other considerations such ascustom or economy. Also, this step may be performed temporallyindependent of other steps in the method. If the same considerationapplies for all the identified parameters under consideration, the sameset of threshold values may be used. Otherwise, one may choose to usedifferent threshold values for different parameters.

FIG. 5 depicts the relationship between values of an equivalency indexand the corresponding shift of two probabilty distribution curves thatgenerate the equivalency index. Element 501 depicts the scale ofequivalency indices and element 502 depicts the scale of thecorresponding shift.

In step 315, one compares the equivalency index E_(PA) to the ranges setin step 314. If E_(PA) is in the range above the upper threshold valueof 98%, the passing range or a green zone, one would declare that FAB Ahas achieved a satisfactory equivalency in quality with respect toparameter P. On the other hand, if E_(PA) is in the range below thelower threshold value of 90%. a failing range or a red zone, one woulddeclare that FAB A has not achieved such quality with respect toparameter P. An equivalency index that falls between 98% and 90%, or ayellow zone, usually calls for reviewing of the data and the procedure.

In step 321, one repeats the steps 302 to 315 for all remainingidentified parameters.

In step 322, one declares that the FAB A has achieved the equivalency inquality with respect to the process under test and the quality isacceptable for the production of the product under test if allparameters from FAB A are in the green zone set in step 314.

In step 323, one repeats step 311 to 322 for all other FABs. Any FABthat has all its equivalency indices above the passing threshold valuesor in the green zone would be grouped among the FABs that would bequalified for the production of the product tested.

The disclosures and the description herein are purely illustrative andare not intended to be in any sense limiting. A person skilled in theart of statistical quality control would be able to apply the methoddisclosed in the above embodiments to his or her particular product. Theproduct may be goods or services and the product may be the processitself.

1. A method for qualifying a first product based on an equivalency indexassociated with a characteristic parameter of the product, comprising:a. identifying at least one variable characteristic parameter of thefirst product; b. measuring said parameter on a group of the firstproduct; c. recording the data of the measurement; d. constructing afirst probability distribution from the data; e. repeat step b and c ona group of a second product, the second product being possessive ofknown desirable quality; f. deriving an average value and a standarddeviation from the data taken from the second product; g. performing anintegration of the first probability distribution over limits related tothe average value and standard deviation; h. deriving an equivalencyindex of said variable characteristic parameter based on the result ofthe integration; i. setting a threshold value for the equivalency index;j. comparing the equivalency index to the set threshold value; k.declaring the first product as being of equivalent quality as the secondproduct when the equivalency index of at least one identifiedcharacteristic parameter is not lower than the set threshold value. 2.The method of claim 1 wherein the product are goods of manufacture. 3.The method of claim 1 wherein the product is a service.
 4. A method forqualifying a first process based on an equivalency index associated witha characteristic parameter of a product, the product being manufacturedwith the first process, comprising: a. identifying at least one variablecharacteristic parameter of a product manufactured with the firstprocess; b. measuring said parameter on a first group of productsmanufactured with the first process; c. recording the data of themeasurement; d. constructing a first probability distribution from thedata; e. repeat step b and c on a second group of products, the secondgroup of products being manufactured with a second process and thesecond process being of known desirable quality; f. deriving an averagevalue and a standard deviation from the data taken from the second groupof products; g. performing an integration of first probabilitydistribution over limits related to the average value and the standarddeviation; h. deriving an equivalency index of said variablecharacteristic parameter based on the result of the integration; i.setting a threshold value for the equivalency index; j. comparing theequivalency index to the set threshold value; k. declaring the firstprocess as being of equivalent quality as the second process when theequivalency index of at least one identified characteristic parameter isnot lower than the set threshold value.
 5. The method of claim 4 whereinthe process is for manufacturing a semiconductor integrated circuit. 6.The method in claim 4 wherein the product is a semiconductor integratedcircuit.
 7. A method for qualifying a product based on an equivalencyindex associated with a characteristic parameter of the product,comprising: a. identifying at least one variable characteristicparameter of the product; b. measuring said parameter on a group of theproducts; c. recording the data of the measurement; d. constructing afirst probability distribution from the data; e. providing a desiredtarget average value and a desired standard deviation value; f.performing an integration of the first probability distribution overlimits related to the desired target average value and the desiredstandard deviation value; g. deriving an equivalency index of saidvariable characteristic parameter based on the result of theintegration; h. setting a threshold value for the equivalency index; i.comparing the equivalency index to the set threshold value; j. declaringthe product as being of quality meeting the average and standarddeviation targets when the equivalency index of at least one identifiedcharacteristic parameter is not lower than the set threshold value. 8.The method in claim 7 wherein the product are goods of manufacture. 9.The method in claim 7 wherein the product is a service.
 10. A method forqualifying a first process based on an equivalency index associated witha characteristic parameter of a product, the product being manufacturedwith the first process, comprising: a. identifying at least one variablecharacteristic parameter of a product manufactured with said process; b.measuring said parameter on a first group of products manufactured withsaid process; c. recording the data of the measurement; d. constructinga first probability distribution from the data of the measurements; e.providing a desired target average value and a desired standarddeviation value; f. performing an integration of the first probabilitydistribution over limits related to the desired target average value andthe desired standard deviation value; g. deriving an equivalency indexof said variable characteristic parameter based on the result of theintegration; h. setting a threshold value for the equivalency index; i.comparing the equivalency index to the set threshold value; j. declaringthe first process as being of quality meeting the average and standarddeviation targets when the equivalency index of at least one identifiedcharacteristic parameter is not lower than the set threshold value. 11.The method in claim 10 wherein the process is a process formanufacturing a semiconductor integrated circuit.
 12. The method inclaim 10 wherein the product is a semiconductor integrated circuit. 13.A method for declaring two products, a first product and a secondproduct, as being equal, based on an equivalency index associated with acharacteristic parameter common to the two products, comprising: a.identifying at least one variable characteristic parameter common to thetwo products; b. measuring said parameter on a group of the firstproduct; c. recording the data of the measurement; d. constructing afirst probability distribution from the data; e. determining a firstaverage value and a first standard deviation of said first probabilitydistribution; f. repeating steps b through c with a group of the secondproduct; g. constructing a second probability distribution from the dataof measurements taken from the group of the second product; h.determining an second average value and a second standard deviation ofthe second probability distribution; i. performing an integration of thesum of the two probability distributions over limits related to thefirst and second average values and the first and second standarddeviations; j. deriving an equivalency index of said variablecharacteristic parameter based on the result of the integration; k.setting a threshold value for the equivalency index; l. comparing theequivalency index to the set threshold value; m. declaring said twoproducts as being equivalent in quality when the equivalency index of atleast one identified characteristic parameter is not lower than the setthreshold.
 14. The method in claim 13 wherein the two products are goodsof manufacture.
 15. The method in claim 13 wherein the two products areservices.
 16. A method for declaring two processes, a first process anda second process, as being equal, based on an equivalency indexassociated with a characteristic parameter to a product manufacturedwith the two processes, comprising: a. identifying at least one variablecharacteristic parameter of the product, the product being manufacturedwith the two processes; b. measuring said parameter on a first group ofthe product, the first group of the product being manufactured with thefirst process; c. recording the data of the measurement; d. constructinga first probability distribution from the data in step c; e. determininga first average value and a first standard deviation of said firstprobability distribution; f. repeating steps b and c on a second groupof the product, the second group of the product being manufactured witha second process; g. constructing a second probability distribution fromthe data taken from the second group of product; h. determining ansecond average value and a second standard deviation of said secondprobability distribution; i. performing an integration of the sum of thetwo probability distributions over limits related to the first andsecond average values and the first and second standard deviations; j.deriving an equivalency index of said variable characteristic parameterbased on the result of the integration; k. setting a threshold value forthe equivalency index; l. comparing the equivalency index to the setthreshold value; m. declaring said two facilities as possessive of saidprocess of equivalent quality when the equivalency index of at least oneidentified characteristic parameter is not lower than the setthresholds.
 17. The method of claim 16 wherein the two processes are formanufacturing a semiconductor integrated circuit.
 18. The method ofclaim 16 wherein the product is a semiconductor integrated circuit. 19.A method for declaring a plurality of products as being equivalent inquality, based on an equivalency index associated with a characteristicparameter common to the plurality of products, comprising: a.identifying at least one variable characteristic parameter common to theplurality of products; b. measuring said parameter on a group of a firstproduct of the plurality of products; c. recording data of themeasurement; d. constructing a first probability distribution from thedata; e. determining a first standard deviation of said firstprobability distribution; f. repeating steps b and c on a group of asecond product of the plurality of products; g. constructing a secondprobability distribution from the data; h. determining a second standarddeviation of said second probability distribution; i. repeating steps fand g for the remaining of the plurality of products; j. providing adesired target value for said parameter; k. integrating the firstprobability distribution over a pair of limits, the pair of limits beingrelated to the desired target value; l. deriving an equivalency index ofsaid variable characteristic parameter based on the result of theintegration; m. setting a threshold value for the equivalency index; n.comparing the equivalency index to the set threshold value; o. repeatingsteps k, l, and n for each of the remaining plurality of products; p.declaring each of the plurality of products as having achieved theequivalency in quality and the quality being satisfactory when at leastone equivalency index associated with the each of the plurality ofproducts is not lower than the set threshold value.
 20. The method ofclaim 19 wherein the plurality of products are goods of manufacture. 21.The method of claim 19 wherein the plurality of products are services.22. A method for declaring a plurality of processes as being equivalentin quality, based on an equivalency index associated with acharacteristic parameter of a product manufactured with said processes,comprising: a. identifying at least one variable characteristicparameter of the product manufactured with said processes; b. measuringsaid parameter on a first group of products, the products beingmanufactured with a first process of the plurality of processes; c.recording data of the measurement; d. constructing a first probabilitydistribution from the data; e. determining a first standard deviation ofsaid first probability distribution; f. repeating steps b and c on asecond group of products, the second group of products beingmanufactured with a second process of the plurality of processes; g.constructing a second probability distribution from the data; h.determining a second standard deviation of said second probabilitydistribution; i. repeating steps f through h for the remaining of theplurality of processes; j. providing a desired target value for saidparameter; k. integrating the first probability distribution over a pairof limits, the pair of limits being related to the desired target value;l. deriving an equivalency index of said variable characteristicparameter based on the result of the integration; m. setting a thresholdvalue for the equivalency index; n. comparing the equivalency index tothe set threshold value; o. repeating steps k, l, and n for each of theremaining plurality of processes; p. declaring each of the plurality ofprocesses as having achieved the equivalency in quality and the qualitybeing satisfactory when at least one equivalency index associated withthe each of the plurality of processes is not lower than the setthreshold value.
 23. The method in claim 22 wherein the plurality ofprocesses is for making semiconductor integrated circuits.
 24. Themethod of claim 22 wherein the product is a semiconductor integratedcircuit.